Publication Date:
2013-04-11
Description:
In this paper, given $f:\left[ a,b\right] \times \left( C\left( \left[ a,b%\right] \right) \right) ^{n-2}\times \mathbb{R}^{2}\rightarrow \mathbb{R}$ a$L^{1}-$Carath\'{e}odory function, it is considered the functional higherorder equation\begin{equation*}u^{(n)}\left( x\right) =f(x,u,u^{\prime },...,u^{\left( n-2\right) }\left(x\right) ,u^{\left( n-1\right) }\left( x\right) )\end{equation*}%together with the nonlinear functional boundary conditions, for \ $%i=0,...,n-2$%\begin{equation*}\begin{array}{l}L_{i}(u,u^{\prime },...,u^{\left( n-1\right) },u^{\left( i\right) }\left(a\right) )=0,\text{ } \\L_{n-1}(u,u^{\prime },...,u^{\left( n-1\right) },u^{\left( n-2\right)}\left( b\right) )=0,%\end{array}%\end{equation*}Here $L_{i}$, $i=0,...,n-1$, are continuous functions. It will be proved anexistence and location result in presence of not necessarily ordered lowerand upper solutions, without assuming any monotone properties on theboundary conditions and on the nonlinearity $f.$
Print ISSN:
1687-2762
Electronic ISSN:
1687-2770
Topics:
Mathematics
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